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Thermomechanical anisotropy and flowability of talc and glass fiber reinforced multiphase polymer composites
Accepted Manuscript Thermomechanical Anisotropy and Flowability of Talc and Glass Fiber Reinforced Multiphase Polymer Composites Doo Jin Lee, Young Seok Song PII: DOI: Reference:
S0263-8223(17)31144-3 http://dx.doi.org/10.1016/j.compstruct.2017.04.065 COST 8496
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
10 April 2017 23 April 2017 25 April 2017
Please cite this article as: Lee, D.J., Song, Y.S., Thermomechanical Anisotropy and Flowability of Talc and Glass Fiber Reinforced Multiphase Polymer Composites, Composite Structures (2017), doi: http://dx.doi.org/10.1016/ j.compstruct.2017.04.065
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Thermomechanical Anisotropy and Flowability of Talc and Glass Fiber Reinforced Multiphase Polymer Composites
Doo Jin Lee1 and Young Seok Song2*
1
Ceramic Fiber and Composite Materials Center, Korea Institute of Ceramic Engineering and Technology, 101 Soho-ro, Jinju-si, Gyeongsangnam-do, 52851, Korea. 2
* Department of Fiber System Engineering, Dankook University, 152 Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do, 16890, Korea
Tel.: +82-31-8005-3567; Fax: +82-31-8005-2209; E-mail: [email protected]
Abstract For fillers reinforced polymer composites, the material properties of the composites are affected by the dispersion and orientation of the inclusions. In particular, high aspect ratio inclusions such as glass fibers in the polymer matrix generate the mechanical or thermomechanical anisotropy of the composites that are critical to the dimensional stability, flowability, toughness, and strength of the final products. We investigate the microstructural anisotropy of multiphase polymer composites composed of talcs and glass fibers to characterize the anisotropic thermomechanical properties of the composites. The internal structure of the composites is observed by using an X-ray microtomography to characterize fiber length distributions. The fiber length distributions are fitted to the
Weibull distribution statistical function to model the ultimate tensile strength of the composites. A fiber efficiency factor is coupled with the statistical function to understand the effect of the fiber length distributions on the mechanical strength of the composites. The thermomechanical anisotropy is evaluated by using linear thermal expansion coefficients. The flowability of molten polymer composites is evaluated experimentally and numerically to evaluate the role of inclusions on rheological properties and processability of the composites.
Keywords: X-ray microtomography, Thermomechanical anisotropy, Fiber length distribution (FLD), Fiber reinforced polymer (FRP) composites, flowability, processability
1. Introduction
Fiber reinforced polymer composites have been extensively studied to design superior engineering materials that possess improved material properties such as high impact and tensile strength, fatigue resistance, high thermal resistance, good interfacial adhesion between reinforcements and matrix, low electrical conductivity, and dimensional stability [1-4]. When inclusions such as fibers and minerals are embedded in a polymer matrix during polymer processing, the polymer composites often show anisotropic mechanical, thermomechanical, and electrical properties owing to the local anisotropy of inclusions [57]. In general, polymer composites are classified into isotropic, transversely isotropic, and anisotropic systems due to their microscopic structures. The isotropic composites represent the ones with the same material properties in all directions. On the other hand, the
transversely isotropic composites are referred to as the ones with symmetric physical properties along a normal axis to a plane of isotropy. A good example of a transversely isotropic material is unidirecionally aligned fiber reinforced composites. There is a general acceptance by many researchers to use the terminology of the anisotropic system to describe the transversely isotropic system. Here, we also represent our transversely isotropic composite systems with the anisotropic systems.
Fibers experience severe breakage during the processes such as extrusion or injection molding due to high pressures and shear stresses. As a result, wide fiber length distributions (FLDs) take place, which affects the physical properties of the polymer composites significantly [8, 9]. FLDs in fiber reinforced polymer composites are a key factor to determine their anisotropic material properties of the composites such as mechanical, thermomechanical, and electrical anisotropy. Several techniques for observing the internal structures of polymer composites have been developed such as confocal laser scanning microscopy [10-12], scanning electron microcopy (SEM), and X-ray microtomography [1316]. The confocal laser microscopic technique has its limit on low spatial resolution to analyze three-dimensional complex shape geometries, and the scanning electron microscopy only measures a local region of interest. Of these techniques, the X-ray microtomography has been gaining much attentions due to its high-resolution, nondestructive testing, and easy sample preparation. This technique basically scans a large number of two dimensional cross-section images, and stacks them to reconstruct a three dimensional volume. The reconstructed volume can offer a 3D internal structure with high spatial resolution. FLDs can be measured with this technique to anticipate the physical
properties of the polymer composites such as mechanical stiffness, strength, thermal expansion coefficient, and electrical conductivity [17-22].
FLDs in composites can also affect their rheological behaviors as they flow into a mold during a polymer processing such as an injection molding, compression molding, extrusion, etc. Especially, a good flowability of the molten polymer composites is highly desirable for a micro-injection molding process that produces micro-scale products widely used in industrial applications such as multi-functional lab-on-a-chips, micro-connectors in smartphones, micro-actuators in various electronic components. Therefore, it is important to enhance the flowability of the molten polymer composites by analyzing the rheological characteristics of the molten polymer composites. Among super engineering plastics, liquid crystalline polymers (LCPs) are widely used in industrial applications for key components including automobiles and electronics appliance products such as smartphones, PCs and air conditioners. LCPs have unique features such as good flowability, heat and flame resistance, high rigidity, good dimensional stability, and low warpage due to their molecular orientations upon the flow. Inclusions such as glass fibers and talcs are often added to LCPs to enhance their mechanical and thermal properties. However, the reinforcing process deteriorates the flowability due to increased viscosity and high friction caused by the inclusions during the flow in a mold. Therefore, it is necessary to investigate the effects of inclusions on thermomechanical and rheological properties.
In this work, we explored the effects of FLDs on thermomechanical anisotropy and flowability of talc and glass fiber reinforced multiphase LCP composites. The internal
structures of the polymer composites were examined by using an X-ray microtomography to analyze the FLDs and fiber alignments. The ultimate tensile strengths of the composites with different FLDs were examined and theoretically calculated to investigate the effect of FLDs on the mechanical properties. The flowability of the composites with different mean fiber lengths was also evaluated experimentally and numerically.
2. Experimental
2.1. Materials and Sample characterization Three commercially available Liquid Crystalline Polymers (LCPs) (6130GM, 6040GM, and 6000A, Ueno Japan) are used for experiments. LCP 6130GM and LCP 6040GM are talc and glass fiber filled multiphase polymer composites, while LCP 6000A is a pure LCP without any inclusion. The test samples of 6130GM and 6040GM are denoted as TS 1 and TS 2, respectively. Thin tensile (10 mm in width × 1 mm in height) specimens are produced to generate unidirecionally fiber aligned tensile testing samples. Spiral-shape specimens (650 µm in width × 1500 µm in height) are produced to investigate the flowability of the molten polymer composites. These two specimens are produced by using an injection molding machine (SE18D, Sumitomo). TS 1 and TS 2 are incinerated at 600 ℃ for 24 hours in a furnace (L15/11/P320, Nabertherm) under ambient air environment to characterize the amount of total inclusions inside the samples. An inductively coupled
plasma (ICP) mass spectrometer (ELAN 6100, Perkin-Elmer) is used to investigate each sample amount of talcs and glass fibers in TS 1 and TS 2.
2.2. Thermal properties The thermal properties of the samples are investigated by using a differential scanning calorimeter (DSC) (DSC-7, Perkin-Elmer). The samples are heated from 20 to 300 ℃, and then cooled to 30 ℃ at a rate of 10 ℃/min to eliminate any thermal history. Thereafter, they are reheated to 300 ℃ to capture the glass transition temperature. All the procedures for DSC are performed under nitrogen. A thermomechanical analyzer (TMA) (TMA-Q400, TA instrument) is used to measure the linear thermal expansion coefficients of samples under ASTM E831 standard test method. A heating rate is set to be 5 ℃/min in the temperature range of 30 to 250 ℃ under nitrogen.
2.3. Micro-CT imaging and image processing The morphology of samples is characterized by using a field emission scanning electron microscope (FE-SEM) (JSM-6390LV, JEOL). A high-resolution X-ray microtomography system (Micro-CT 1172, Skyscan) is employed to acquire FLDs of the testing samples. A 100 kV and 10 Mp X-ray source is used to carry out two-dimensional image analysis and three-dimensional reconstruction with a resolution of 3 µm. Collected images are processed
by using a commercial image analysis tool (Image-Pro Plus 7.0, Media Cybernetics) to obtain FLDs from the micro-CT images.
2.4. Mechanical testing The thin tensile specimens produced are tested to measure the strain-stress curves. Tensile testing is carried out at least five times for each specimen by using a universal tensile machine (UTM) (8801, Instron). A crosshead speed is set to be 5 mm/min according to ASTM D638.
2.5. Flowability test A spiral-shaped mold with a long rectangular channel of 650 µm in width and 1500 µm in height is used to characterize the flowability of the molten polymer composites. The molten TS 1 and TS 2 are injected into the mold. Processing conditions for the injection molding process was listed in SI Table 1. A flow length which represents the flowability is measured and compared with numerical simulation results. For a numerical simulation, a commercial software (Moldflow 2010, Autodesk) is used. The Cross-WLF model is used to describe the temperature and shear rate dependencies of the viscosities. For TS 1 and TS 2, the mean fiber lengths and the amount of talcs and glass fibers obtained by experiment were used in the numerical simulation.
3. Theoretical background 3.1 Fiber length distribution (FLD) For fiber reinforced polymer (FRP) composites, the length of fibers can vary due to shear stresses that cause the breakage of the fibers during extrusion and injection molding processes. The thermomechanical properties of FRP composites are affected by the FLDs that can be described with a probability density function (PDF). A cumulative function of the fibers is obtained by integrating the PDF with the fiber lengths ranging from to , which is expressed as below.
= = 1
(1)
where, is the fiber length probability density function. The FLD is well described with a two-parameter statistical function, namely the Weibull distribution function that is described as below.
= exp− > 0 & , > 0
(2)
Here, a is the scale parameter and b is the shape parameter. It is important to consider the FLDs to predict thermomechanical properties of the composites such as stiffness, strength, toughness, fatigue resistance, and thermal expansion coefficient. These thermomechanical properties can vary due to the existence of inclusions since the inclusions induce a stressstrain perturbation in the composites [23, 24]. Once the PDFs are known, the mean fiber length can easily be obtained by
%
$ = = & Γ1⁄ + 1
(3)
where Γ* is the gamma function. By knowing the mean fiber length, scale and shape parameters, the ultimate tensile strength of unidirectional fiber reinforced composites with different FLDs can be estimated.
3.2 Mechanical strength of composites When inclusions such as talcs and glass fibers are introduced into a polymer matrix, average strain near the inclusions is not the same with that of the pure matrix [23, 24]. In our composite system, the amount of strain perturbation induced by talcs is first considered to create an effective matrix (Fig. 1a and 1b). The rule of mixture provides a theoretical upper- and lower-bound on material properties such as the elastic modulus, ultimate tensile strength, thermal conductivity, and electrical conductivity. We use the general rule of $--
mixture of +, = ./ +/, + . +, to create the effective matrix composed of a polymer matrix and talcs. Here, ./ and . are the volume fractions of talcs and matrix, and +/, and +, are the ultimate tensile strengths of talcs and matrix, respectively. The ultimate tensile strength of composites for unidirecionally aligned fibers, +0, , can be estimated by the summation of the fiber length contribution on the composite strength. 2
$--
+0, = ∑2 . + + . +, - -,
(4)
$--
where, .- and . are the volume fractions of fibers and matrix, and +-, and +, are the ultimate strengths of fiber and effective matrix, respectively. The ultimate tensile strength of composites can be replaced with an integral form by combining as below.
$--
$--
+0, = .- ⁄$ +-, + . +, = χ.- +-, + . +,
(5)
Here, χ is a fiber efficiency factor that determines the ultimate tensile strength of composites. For unidirectional discontinuous composites, χ < 1 and determined by the critical fiber length 0 which is given by 0 = 5- +0, /7 , where 5- and 7 are the fiber radius and the interfacial shear stress between matrix and fiber. When the fiber length is uniform, the fiber efficiency factor χ = /20 for < 0 and χ = 1 − 0 /2 for ≥ 0 . However, this condition is not true in real cases since the fibers are broken during the processing. Therefore, it is necessary to consider the fiber length distributions in the composites to predict precise thermomechanical properties. In our case, the fiber length is not uniform and the fibers are distributed in the matrix with talcs. Therefore, the interfacial shear stress between the fibers and the effective matrix will increase with respect to the applied tensile stress. When tensile force is applied to the composite, the fibers act as bridges across the crack plane. When the fiber length is not uniform, χ is modified as below [25].
χ = = :; ⁄20 $ < + ⁄$ :1 − 0 /2<
=
(6)
Here, χ can be obtained if , , 0 and are obtained. These parameters are obtained from experiment. Overall, the composites consist of the effective matrix and the
anisotropic glass fibers with fiber length distributions (Fig. 1c). The ultimate tensile strength of composites is calculated by combining Eq. 5 and Eq. 6.
4. Results and discussion 4.1 Quantification of fiber length distribution Reinforcing fillers are commonly used to improve the mechanical properties of polymer composites. It is well known that glass fibers and carbon fibers can enhance the mechanical strength as much as ten times to fifty times. Different aspect ratios of the inclusions in the polymer matrix affect the concentrated force and shear resistance between the matrix and inclusions. Therefore, it is crucial to examine the effect of FLDs on mechanical properties [16, 26-28]. In this study, glass fibers and talcs are included in TS 1 and TS 2 samples. TS 1 and TS 2 are incinerated under air condition to examine the amount of the inclusions in the multiphase polymer composites. The weight fraction of the inclusion is defined as >? − > − > @ ⁄>? × 100, where >? , >, and > @ are the weight of original sample, the weight of crucible and original sample, and the weight of crucible and residue after incinerating the sample. The total weight fractions of the inclusions in TS 1 and TS 2 were measured to be 29.06 wt% and 37.93 wt% which correspond to 17 vol% and 25 vol%, respectively (Fig. 2). It was also verified by using an inductively coupled plasma (ICP) mass spectrometer that each TS 1 and TS 2 contained almost the same amounts of glass fibers and talcs in each sample (Supplementary Information Fig. 1). Therefore, the total amount of glass fibers in TS 1 and TS 2 composite is 8.5 vol% and 12.5 vol%, respectively.
Since the amount of inclusions embedded in TS 1 and TS 2 is different, their thermomechanical and rheological properties will become different, and the flowability of the composites will also change. It is clear to identify by SEM that TS 1 and TS 2 have glass fibers and talcs, and the glass fibers possess broad length distributions (Fig. 2). It is shown that TS 2 has more amount of glass fibers and talcs in the matrix than in TS 1. However, it is not yet clear to evaluate the FLDs in the matrix. To overcome this issue, the FLDs in the composites were observed by using an X-ray tomographic method. Thin tensile specimens (10 mm in width × 1 mm in height) were produced to generate unidirectional fiber alignments along the flow direction (Fig. 3a). A small piece (10 mm in width × 10 mm in depth × 1 mm in height) was cut at the center of the tensile specimen where unidirectional fiber alignments were produced and a crack takes place. Images of each plane were firstly obtained, and enhanced by controlling the brightness and contrast, transformed into binary images by a thresholding method. The images were stacked along z-axis to reconstruct and analyze the fiber alignment (Fig. 3b and 3c). It was confirmed from the 3D volumetric reconstruction that most of the glass fibers were aligned along the flow direction. Also, the overall length and density of glass fibers in TS 1 seem to be longer and less than in TS 2. Since the FLDs can influence the thermomechanical and rheological properties of products, the quantification of the FLDs should be carried out to understand the relationship between the FLDs and the flowability of molten polymer composites. From the micro-CT images, we experimentally obtained the FLDs (vertical bars in Fig. 3d). It is obvious from the measurement of the probability density functions that the FLDs in TS 1 varies from 10 to 1200 µm while the FLDs in TS 2 ranges from 10 to 500 µm. The
two-parameter Weibull distribution function (Eq. 2) was used to estimate the PDFs of TS 1 and TS 2 composites. The PDFs are useful to evaluate the thermomechanical and local anisotropy of the composites which result in enhanced stiffness, strength, toughness, fatigue resistance, and low thermal expansion coefficients. The experimental results of FLDs are well fitted to Eq. 2, and the relevant parameters are obtained (solid lines in Fig. 3d). FLDs in TS 1 are more broadly distributed than in TS 2, which can support that TS 1 has better mechanical properties. The broad FLDs in TS 1 can also explain big differences in thermal expansion coefficients along the parallel and vertical directions than those of TS 1, which will be explained in section 3.2.
3.2. The effect of inclusions on thermomechanical anisotropy It has been reported that there is an interrelation between the elastic modulus and thermal expansion coefficient of solid materials [29]. The thermomechanical anisotropy of solid materials is of great interest to the engineering field since dimensional stability is important to produce precise engineering components under varying load and temperature. Specially, transversely isotropic glass fibers can generate the anisotropic thermomechanical properties of polymer composites, which requires the characterization of FLDs to understand the role of the inclusions in the composites. Once FLDs are obtained quantitatively by an X-ray tomography, the effective elastic moduli and ultimate tensile strengths of polymer composites can qualitatively be predicted by using statistical FLD functions such as the Weibull distribution, Log-normal, or
Generalized Extreme Value (GEV) functions [16]. We previously reported that FLDs and distribution skewness in polymer composites have significant impacts on the effective elastic moduli of the composites. When glass fibers are included into a polymer matrix, average strains around the fibers are not equal to those of the matrix. Fibers act as bridges transferring interfacial shear stresses between fibers and matrix, which can also be expressed in a similar fashion with the elastic modulus. Therefore, the FLDs of the composites can be a crucial parameter determining their stiffness and ultimate tensile strength. The fiber efficiency factor χ in Eq. 6 was calculated with the FLDs of TS 1 and TS 2 composites experimentally obtained (Fig. 4a). It is confirmed that the value of χ for TS 2 decreases faster than that of TS 1 because the FLDs of TS 2 is more largely skewed (meaning, left-shifted). When the skewness is small, inclusions act as an efficient reinforcement [16]. It is expected that the large skewness of the FLDs for TS 2 may cause low mechanical properties of the composite. In addition, the fibers longer than the critical fiber length 0 have larger contribution to the composite strength than those of short fibers, which means the ultimate tensile strengths of FRP composites decreases with increasing 0 . This is because 0 is inversely proportional to the interfacial adhesion strength [25, 30]. The value of χ rapidly increases with increasing the mean fiber length $ and approaches gradually a plateau level at large mean fiber length (an inset in Fig. 4b). From the χ result, it is anticipated that the ultimate tensile strength of FRP composites would increase significantly until $ reaches 0.2 mm. As expected, the ultimate tensile strength of FRP composites rapidly increases with increasing $ when $ is small, then the increase shows a plateau level around $ = 1 mm (Fig. 4b). In our experiment,
the mean fiber lengths of TS 1 and TS 2 are calculated to be 0.082 mm and 0.05 mm, respectively. From the theory, the tensile strengths of the composites for $ = 0.082 mm and 0.05 mm correspond to +0, = 111 MPa and 98 MPa (see SI Table 2). The experimental results show that the ultimate tensile strengths of TS 1 and TS 2 are around 110 ± 5 MPa and 95 ± 6 MPa, the results of which are in good agreement with the theoretical prediction. One of the possible reasons for higher composite strength for TS 1 than TS 2 is that the overall fiber length in TS 1 are longer than TS 2, promoting good interfacial shear strength 7 between the matrix and fibers, which results in higher ultimate tensile strength of TS 1 than TS 2. It was also reported that the effect of molten polymer flow direction on fatigue behavior for talc-filled composite where the fatigue strength was higher in the longitudinal direction as compared to the transverse to the molten polymer flow direction [31]. The effect was much less as compared to what has been observed for fiber reinforced composites. This behavior can be explained by the concept of a stress transfer length over which the strain in the fiber builds up. Provided that the composite remains fully elastic and there is no interfacial sliding between the fillers and the matrix, the composites with high aspect ratio of the fibers exhibit long stress transfer lengths, providing an efficient reinforcing effect. One of the key factors determining dimensional stability and deflection of polymer composite products is the coefficient of thermal expansion (CTE) [32-34]. Especially, the ratio of anisotropic CTE values strongly influences the warpage and deflection of injection molded polymer composites. A small piece (10 mm in width × 3 mm in depth × 1 mm in height) was cut at the center of the tensile specimen where unidirectional fiber alignments
were produced to measure the CTEs along parallel and vertical directions (An inset in Fig. 5). In our experimental results, there are three unique features to highlight for the CTEs of TS 1 and TS 2 (Fig. 5). First, the CTEs of TS 1 measured in both parallel and vertical directions show higher values than those of TS 2. It is because the total amount of inclusions suspended in TS 2 is higher than TS 1, resulting in the decrease of CTEs upon the temperature change. Second, it is also worthy to note that the CTEs in parallel directions for both TS 1 and TS 2 are much smaller than those in vertical directions. Most of the glass fibers are aligned along the parallel direction to the flow in the composites during the injection molding process while producing the tensile specimens, which hinders the expansion of the composites along the parallel direction. Furthermore, the molecular orientation of LCP itself is also aligned along the parallel direction, which enhances the anisotropy of the CTEs in the composites [34]. Talcs are structurally isotropic reinforcements which do not affect the anisotropy of CTEs of the composites. Third, the difference of the CTEs between parallel and vertical directions for TS 1 is larger than that of TS 2, the result of which can be interpreted from the FLD results. TS 2 shows shorter fiber lengths (meaning, left-shifted FLD distribution) in comparison with TS 1, which induces a small local anisotropy of TS 2 than TS 1 resulting in small increase of the CTEs of the composites.
3.3. The effect of inclusions on glass transition temperature
Since LCPs are highly molecular oriented polymers, they possess unique features such as high mechanical strength at high temperature, extreme chemical resistance, flame retardance, and good flowability. Typically, LCPs show a small glass transition temperature (FG ) than many other polymers due to their high crystallinity, and therefore, the mechanical properties do not significantly change upon the temperature variation. When the inclusions are embedded into the polymer matrix, however, FG changes due to the perturbation of heat capacity caused by the inclusions. FG of pure LCP, TS 1, and TS 2 were examined to characterize the thermodynamic effect of glass fibers on the composites. The samples were first heated up and cooled down as a first cycle to eliminate any thermal history caused during a sample fabrication process. Thereafter, it heated up again to measure the glass transition temperature. It was shown that the pure LCP, TS 1, and TS 2 showed their onsets of FG at 252.97, 246.77, and 240.55 ℃, respectively (Fig 6a – 6c). FG decreases as increasing the amount of inclusions in the LCP matrix. The decrease in the glass transition temperature with high loading of the fillers may indicate the poor interfacial adhesion between the fillers and the matrix. A main reason for the alternation of the glass transition temperature is the changes in the conditions of deformations of the polymer between fillers and the restriction in the molecular mobility due to absorption interaction in polymer surface layers onto filler [35-36]. The formation of an interphase affects the physiochemical properties of the composites. It was also reported that the filler content and the filler size do not significantly affect the glass transition temperature [37]. The existence of reduced FG can lead to poor long term performance of the polymer composites such as lower fracture toughness, durability, and local stress state of the composites [38], which means that TS 1
and TS 2 may have worse long term fracture toughness than the pure LCP matrix even though the tensile strength and elastic moduli are higher than the pure LCP matrix. These results are associated with the fact that the pure LCP matrix already possesses a good toughness while the inclusion reinforced TS 1 and TS 2 composites did not improve the toughness of the composites rather than enhancing the elastic moduli and ultimate tensile strengths only. This behavior is often observed in FRP composites where the polymer matrix has a good fracture toughness so that there is no improvement on the fracture toughness comparing to the pure polymer matrix [38].
3.4. The effect of inclusions on flowability An injection molding process of molten polymer composites is modelled by the finite element method (FEM). The governing equations of the process are the conservations of mass, momentum, and energy, which are described as below. MN M/
+ O∇ ∙ RS = 0
MTS
O M/ = −∇U + ∇ ∙ 7 + OVS MY
M[
OWX M/ = ZF M/ + \]^ ; + ∇ ∙ _S
(7)
(8)
(9)
where O is the density, RS is the velocity vector, P is the pressure, 7 is the viscous stress tensor, VS is the body force vector, WX is the specific heat at constant pressure, Z is the coefficient of thermal expansion, \ is the viscosity, ]^ is the shear rate, and _S is the heat flux.
The molten polymer is considered as a non-Newtonian viscous fluid which can be represented by the Cross-WLF model as below. \=
`a da e^ %i bc ∗ h f
(10)
where \, \? , ]^ , 7 ∗ , and n represent the melt viscosity, the zero shear viscosity, the shear rate, the critical stress level at the transition to shear thinning, and the power law index in high shear rate regime. Flowability is especially an important issue for a micro-injection molding process of small components such as electronic components, connectors, antennas wherein molten polymers pass through extremely narrow channel pitches. The flowability of molten polymers strongly depends on the composition of the polymer composites since the inclusions in the matrix affect their rheological properties and solidification process. We prepared a narrow spiral-shaped mold with the rectangular cross-section of 650 µm in width and 1500 µm in height to measure the flowability of TS 1 and TS 2 composites (Fig. 7a). A flow length is defined as the distance inside the spiral mold through which molten polymers flow until they solidify. It is shown that TS 1 flows farther than TS 2 in the mold until the flow front is solidified (An inset of Fig. 7b). The reinforcing fillers inside the matrix affect the rheological properties of the molten polymers. There are three main parameters that determine the solidification process of molten polymers: thermal conductivity, specific heat, and viscosity of composites. The thermal conductivity and the specific heat of TS 1 and TS 2 are similar so that the viscosity of composites primarily
affects the flowability of the molten composites inside a mold. Processing conditions (e.g., mold temperature, melt temperature, filling and packing pressures) for an injection molding of TS 1 and TS 2 set to be the same to compare only the viscosity effect on the flowability. The viscosity parameters for fitting to the Cross-WLF viscosity model are listed in SI Table 3. It is confirmed that the flowability of TS 1 is better than TS 2 since the viscosity of TS 1 lower than that of TS 2 at low shear rate range under the same temperature (Fig. 7b). When the viscosity of the material is low at certain temperature, the molten polymers can easily be filled into the mold. TS 1 composite with the smaller amount of glass fibers than TS 2 showed a lower viscosity, promoting better flowability (Fig. 7c – 7f). There is a cross-over point at shear rate 4000 s-1, which is thought to occur because the molten composite with relatively short fiber lengths in TS 2 possesses a low friction than TS 1 when the shear rate exceeds a critical point even though the fiber concentration is higher than TS 1. In our experiment, the maximum shear rate occurs in the mold is around 2500 s-1 so that the flowability of TS 1 is still better than TS 2. Also the length of glass fibers does not affect the flowability significantly since the dimensions of the spiral mold are much longer than the fiber lengths. The effect of FLDs will become more critical for a micro-injection molding process where the dimensions of the mold are small and shear rates are extremely high. Overall, this work will help understand the effects of FLDs on thermomechanical anisotropy and rheological properties of polymer composites that are ubiquitous in a variety of industrial applications, and give good insights to improve the processability of polymer
composites during various molten polymer processing such as injection molding, compression molding, resin transfer molding, infusion, and extrusion techniques.
4. Conclusion We investigated the microstructural anisotropy of glass fiber and talc reinforced multiphase polymer composites. The inclusions in the polymer matrix affect the anisotropic thermomechanical properties and rheological behaviors of the composites. The microstructure was analyzed by an X-ray microtomography to investigate the fiber length distributions. The Weibull statistical function was employed to characterize the fiber length distributions. The fiber efficiency factor was calculated by using the statistical function and was used to model the ultimate tensile strength of the composites. It was confirmed that the ultimate tensile strength of the composites increases when the fiber efficiency factor increases due to the long fiber lengths. The theoretical prediction was in good agreement with the experimental result. The thermomechanical anisotropy was evaluated by using linear thermal expansion coefficients. The structural hindrance due to the fibers reduced the thermal expansion along the fiber alignment direction, resulting in thermomechanical anisotropy of the composites. The glass transition temperature was found to decrease with increasing the amount of inclusions into the polymer matrix. The rheological properties of the molten polymer composites were confirmed to be a primary factor in determining the flowability of the composites. This work will help understand the effects of FLDs on thermomechanical anisotropy and flowability, which gives good insights to improve the processability of inclusion reinforced polymer composites.
Acknowledgement This work was supported by Project of convergence/integrated technology development funded by Korea Small and Medium Business Administration in 2015. It was partially supported by Basic Research Program through the National Research Foundation of Korea (NRF)
funded
by
the
Ministry
of
Education,
Science
and
Technology
(2015R1A6A3A03020612 and 2013R1A1A2059827). Also, this work was supported by the Commercializations Promotion Agency for R&D Outcomes (COMPA) funded by the Ministry of Science, ICT and Future Panning (MISP). It was supported by the Industrial Strategic Technology Development Program funded by the Ministry of Trade, Industry and Energy (MI, Korea) [10052641].
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[17] Agari Y, Ueda A, Nagai S. Thermal conductivity of a polyethylene filled with disoriented short‐cut carbon fibers. Journal of Applied Polymer Science. 1991;43(6):111724. [18] Thomason J, Groenewoud W. The influence of fibre length and concentration on the properties of glass fibre reinforced polypropylene: 2. Thermal properties. Composites Part A: Applied Science and Manufacturing. 1996;27(7):555-65. [19] Thomason J, Vlug M. Influence of fibre length and concentration on the properties of glass fibre-reinforced polypropylene: 1. Tensile and flexural modulus. Composites Part A: Applied science and manufacturing. 1996;27(6):477-84. [20] Weber M, Kamal MR. Estimation of the volume resistivity of electrically conductive composites. Polymer composites. 1997;18(6):711-25. [21] Hine PJ, Lusti HR, Gusev AA. Numerical simulation of the effects of volume fraction, aspect ratio and fibre length distribution on the elastic and thermoelastic properties of short fibre composites. Composites science and technology. 2002;62(10):1445-53. [22] Fu SY, Mai YW. Thermal conductivity of misaligned short‐fiber‐reinforced polymer composites. Journal of applied polymer science. 2003;88(6):1497-505. [23] Eshelby JD. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences: The Royal Society; 1957. p. 376-96. [24] Tandon G, Weng G. The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites. Polymer composites. 1984;5(4):327-33. [25] Fu S-Y, Lauke B. Effects of fiber length and fiber orientation distributions on the tensile strength of short-fiber-reinforced polymers. Composites Science and Technology. 1996;56(10):1179-90. [26] Suarez S, Gibson R, Sun C, Chaturvedi S. The influence of fiber length and fiber orientation on damping and stiffness of polymer composite materials. Experimental Mechanics. 1986;26(2):175-84. [27] Chin WK, Liu HT, Lee YD. Effects of fiber length and orientation distribution on the elastic modulus of short fiber reinforced thermoplastics. Polymer Composites. 1988;9(1):27-35. [28] Joshi M, Maiti S, Misra A, Mittal R. Influence of fiber length, fiber orientation, and interfacial adhesion on poly (butylene terephthalate)/polyethylene alloys reinforced with short glass fibers. Polymer composites. 1994;15(5):349-58. [29] Arenz R. Relation of elastic modulus to thermal expansion coefficient in elastic and viscoelastic materials. 23rd Conference and Exposition on Structural Dynamics, Orlando, FL, USA, Society for Experimental Mechanics, Bethel, CT2005. [30] Yu Z, Brisson J, Ait‐Kadi A. Prediction of mechanical properties of short kevlar fiber‐nylon‐6, 6 composites. Polymer composites. 1994;15(1):64-73. [31] Jacques MS. An analysis of thermal warpage in injection molded flat parts due to unbalanced cooling. Polymer Engineering & Science. 1982;22(4):241-7. [32] Eftekhari M, Fatemi A. Fatigue behaviour and modelling of talc‐filled and short glass fibre reinforced thermoplastics, including temperature and mean stress effects. Fatigue & Fracture of Engineering Materials & Structures. 2016;40(3):333-48.
[33] Widhalm C, Tschegg E, Eppensteiner W. Anisotropic thermal expansion causes deformation of marble claddings. Journal of Performance of Constructed Facilities. 1996;10(1):5-10. [34] Oh HJ, Lee DJ, Lee CG, Jo KY, Lee DH, Song YS, et al. Warpage analysis of a micromolded parts prepared with liquid crystalline polymer based composites. Composites Part A: Applied Science and Manufacturing. 2013;53:34-45. [35] Lipatov YS, Babich VF, Rosovizky VF. Effect of filler on the relaxation time spectra of filled polymers. Journal of Applied Polymer Science. 1976;20(7):1787-94. [36] Theocaris PS, Papanicolaou GC. Variation of glass transition temperature with direction in unidirectional glass fiber-reinforced composites. Colloid & Polymer Science. 1980;258(9):1044-51. [37] Schwarzl FR, Bree HW, Nederveen CJ, Struik LC, Van der Wal CW. On the Mechanical Properties of Unfilled and Filled Elastomers. InMECH. AND CHEMISTRY OF SOLID PROPELLANTS, Proc. 4th. Symp. Naval Structural Mechanics, Pergamon Press, New York 1965. [38] Noda I, Rubingh D. The influence of the fiber/matrix interface on local glass transition temperature. Polymer solutions, blends, and interfaces: proceedings of the Procter and Gamble UERP symposium: Elsevier Science Ltd; 1992. p. 339.
Fig. 1. Schematic illustration of multiphase hybrid composite with talcs and glass fibers. (a) Talcs with polymer matrix, (b) an effective matrix composed of talcs and matrix by the rule of mixture, and (c) a hybrid composite with glass fibers aligned along the tensile direction in the effective matrix. Glass fibers have length distributions and bridge between a crack upon an applied force.
Fig. 2. The characterization of inclusion compositions in (a) TS 1 and (b) TS 2 before and after incineration at 600 ℃ for 24 hours, and SEM images after incineration.
Fig. 3. (a) Tensile specimen of LCP composites (X-ray tomography images are obtained from the red rectangular section sized by10 mm in width × 10 mm in depth × 1 mm in height), (b) and (c) 2D tomographic raw images are image-processed, and then reconstructed to 3D structures to observe the fiber alignments and length distributions. (d) Fiber length distributions of TS 1 and TS 2, and their Weibull function curve fittings. A scale bar is 0.1 mm.
Fig. 4. (a) Effect of critical fiber length on fiber efficiency factor for unidirectional composites of TS 1 and TS 2. (b) Effect of mean fiber length on the ultimate tensile strength of composites of TS 1 and TS 2. An inset graph shows a fiber efficiency factor with
respect
to
the
mean
fiber
length.
Fig. 5. The coefficients of thermal expansion of TS 1 and TS 2 along the parallel and vertical directions with respect to fiber alignment direction. The heating rate is 5 ℃/min.
(Continued.)
Fig. 6. DSC traces of (a) pure LCP, (b) TS 1, and (c) TS 2 during first and second heating stages with the heating rate of 10 ℃/min.
Fig. 7. (a) Flowability test in a spiral-shaped mold by using an injection molding. (b) Viscosities of TS 1 and TS 2 at 350 ℃ used in this study. An inset graph shows the flow length of TS 1 and TS 2 through the spiral-shaped mold. (c), (d) Experimental and numerical results of the flow length of TS 1. (e), (f) Experimental and numerical results of the flow length of TS 2.
S0263-8223(17)31144-3 http://dx.doi.org/10.1016/j.compstruct.2017.04.065 COST 8496
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
10 April 2017 23 April 2017 25 April 2017
Please cite this article as: Lee, D.J., Song, Y.S., Thermomechanical Anisotropy and Flowability of Talc and Glass Fiber Reinforced Multiphase Polymer Composites, Composite Structures (2017), doi: http://dx.doi.org/10.1016/ j.compstruct.2017.04.065
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Thermomechanical Anisotropy and Flowability of Talc and Glass Fiber Reinforced Multiphase Polymer Composites
Doo Jin Lee1 and Young Seok Song2*
1
Ceramic Fiber and Composite Materials Center, Korea Institute of Ceramic Engineering and Technology, 101 Soho-ro, Jinju-si, Gyeongsangnam-do, 52851, Korea. 2
* Department of Fiber System Engineering, Dankook University, 152 Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do, 16890, Korea
Tel.: +82-31-8005-3567; Fax: +82-31-8005-2209; E-mail: [email protected]
Abstract For fillers reinforced polymer composites, the material properties of the composites are affected by the dispersion and orientation of the inclusions. In particular, high aspect ratio inclusions such as glass fibers in the polymer matrix generate the mechanical or thermomechanical anisotropy of the composites that are critical to the dimensional stability, flowability, toughness, and strength of the final products. We investigate the microstructural anisotropy of multiphase polymer composites composed of talcs and glass fibers to characterize the anisotropic thermomechanical properties of the composites. The internal structure of the composites is observed by using an X-ray microtomography to characterize fiber length distributions. The fiber length distributions are fitted to the
Weibull distribution statistical function to model the ultimate tensile strength of the composites. A fiber efficiency factor is coupled with the statistical function to understand the effect of the fiber length distributions on the mechanical strength of the composites. The thermomechanical anisotropy is evaluated by using linear thermal expansion coefficients. The flowability of molten polymer composites is evaluated experimentally and numerically to evaluate the role of inclusions on rheological properties and processability of the composites.
Keywords: X-ray microtomography, Thermomechanical anisotropy, Fiber length distribution (FLD), Fiber reinforced polymer (FRP) composites, flowability, processability
1. Introduction
Fiber reinforced polymer composites have been extensively studied to design superior engineering materials that possess improved material properties such as high impact and tensile strength, fatigue resistance, high thermal resistance, good interfacial adhesion between reinforcements and matrix, low electrical conductivity, and dimensional stability [1-4]. When inclusions such as fibers and minerals are embedded in a polymer matrix during polymer processing, the polymer composites often show anisotropic mechanical, thermomechanical, and electrical properties owing to the local anisotropy of inclusions [57]. In general, polymer composites are classified into isotropic, transversely isotropic, and anisotropic systems due to their microscopic structures. The isotropic composites represent the ones with the same material properties in all directions. On the other hand, the
transversely isotropic composites are referred to as the ones with symmetric physical properties along a normal axis to a plane of isotropy. A good example of a transversely isotropic material is unidirecionally aligned fiber reinforced composites. There is a general acceptance by many researchers to use the terminology of the anisotropic system to describe the transversely isotropic system. Here, we also represent our transversely isotropic composite systems with the anisotropic systems.
Fibers experience severe breakage during the processes such as extrusion or injection molding due to high pressures and shear stresses. As a result, wide fiber length distributions (FLDs) take place, which affects the physical properties of the polymer composites significantly [8, 9]. FLDs in fiber reinforced polymer composites are a key factor to determine their anisotropic material properties of the composites such as mechanical, thermomechanical, and electrical anisotropy. Several techniques for observing the internal structures of polymer composites have been developed such as confocal laser scanning microscopy [10-12], scanning electron microcopy (SEM), and X-ray microtomography [1316]. The confocal laser microscopic technique has its limit on low spatial resolution to analyze three-dimensional complex shape geometries, and the scanning electron microscopy only measures a local region of interest. Of these techniques, the X-ray microtomography has been gaining much attentions due to its high-resolution, nondestructive testing, and easy sample preparation. This technique basically scans a large number of two dimensional cross-section images, and stacks them to reconstruct a three dimensional volume. The reconstructed volume can offer a 3D internal structure with high spatial resolution. FLDs can be measured with this technique to anticipate the physical
properties of the polymer composites such as mechanical stiffness, strength, thermal expansion coefficient, and electrical conductivity [17-22].
FLDs in composites can also affect their rheological behaviors as they flow into a mold during a polymer processing such as an injection molding, compression molding, extrusion, etc. Especially, a good flowability of the molten polymer composites is highly desirable for a micro-injection molding process that produces micro-scale products widely used in industrial applications such as multi-functional lab-on-a-chips, micro-connectors in smartphones, micro-actuators in various electronic components. Therefore, it is important to enhance the flowability of the molten polymer composites by analyzing the rheological characteristics of the molten polymer composites. Among super engineering plastics, liquid crystalline polymers (LCPs) are widely used in industrial applications for key components including automobiles and electronics appliance products such as smartphones, PCs and air conditioners. LCPs have unique features such as good flowability, heat and flame resistance, high rigidity, good dimensional stability, and low warpage due to their molecular orientations upon the flow. Inclusions such as glass fibers and talcs are often added to LCPs to enhance their mechanical and thermal properties. However, the reinforcing process deteriorates the flowability due to increased viscosity and high friction caused by the inclusions during the flow in a mold. Therefore, it is necessary to investigate the effects of inclusions on thermomechanical and rheological properties.
In this work, we explored the effects of FLDs on thermomechanical anisotropy and flowability of talc and glass fiber reinforced multiphase LCP composites. The internal
structures of the polymer composites were examined by using an X-ray microtomography to analyze the FLDs and fiber alignments. The ultimate tensile strengths of the composites with different FLDs were examined and theoretically calculated to investigate the effect of FLDs on the mechanical properties. The flowability of the composites with different mean fiber lengths was also evaluated experimentally and numerically.
2. Experimental
2.1. Materials and Sample characterization Three commercially available Liquid Crystalline Polymers (LCPs) (6130GM, 6040GM, and 6000A, Ueno Japan) are used for experiments. LCP 6130GM and LCP 6040GM are talc and glass fiber filled multiphase polymer composites, while LCP 6000A is a pure LCP without any inclusion. The test samples of 6130GM and 6040GM are denoted as TS 1 and TS 2, respectively. Thin tensile (10 mm in width × 1 mm in height) specimens are produced to generate unidirecionally fiber aligned tensile testing samples. Spiral-shape specimens (650 µm in width × 1500 µm in height) are produced to investigate the flowability of the molten polymer composites. These two specimens are produced by using an injection molding machine (SE18D, Sumitomo). TS 1 and TS 2 are incinerated at 600 ℃ for 24 hours in a furnace (L15/11/P320, Nabertherm) under ambient air environment to characterize the amount of total inclusions inside the samples. An inductively coupled
plasma (ICP) mass spectrometer (ELAN 6100, Perkin-Elmer) is used to investigate each sample amount of talcs and glass fibers in TS 1 and TS 2.
2.2. Thermal properties The thermal properties of the samples are investigated by using a differential scanning calorimeter (DSC) (DSC-7, Perkin-Elmer). The samples are heated from 20 to 300 ℃, and then cooled to 30 ℃ at a rate of 10 ℃/min to eliminate any thermal history. Thereafter, they are reheated to 300 ℃ to capture the glass transition temperature. All the procedures for DSC are performed under nitrogen. A thermomechanical analyzer (TMA) (TMA-Q400, TA instrument) is used to measure the linear thermal expansion coefficients of samples under ASTM E831 standard test method. A heating rate is set to be 5 ℃/min in the temperature range of 30 to 250 ℃ under nitrogen.
2.3. Micro-CT imaging and image processing The morphology of samples is characterized by using a field emission scanning electron microscope (FE-SEM) (JSM-6390LV, JEOL). A high-resolution X-ray microtomography system (Micro-CT 1172, Skyscan) is employed to acquire FLDs of the testing samples. A 100 kV and 10 Mp X-ray source is used to carry out two-dimensional image analysis and three-dimensional reconstruction with a resolution of 3 µm. Collected images are processed
by using a commercial image analysis tool (Image-Pro Plus 7.0, Media Cybernetics) to obtain FLDs from the micro-CT images.
2.4. Mechanical testing The thin tensile specimens produced are tested to measure the strain-stress curves. Tensile testing is carried out at least five times for each specimen by using a universal tensile machine (UTM) (8801, Instron). A crosshead speed is set to be 5 mm/min according to ASTM D638.
2.5. Flowability test A spiral-shaped mold with a long rectangular channel of 650 µm in width and 1500 µm in height is used to characterize the flowability of the molten polymer composites. The molten TS 1 and TS 2 are injected into the mold. Processing conditions for the injection molding process was listed in SI Table 1. A flow length which represents the flowability is measured and compared with numerical simulation results. For a numerical simulation, a commercial software (Moldflow 2010, Autodesk) is used. The Cross-WLF model is used to describe the temperature and shear rate dependencies of the viscosities. For TS 1 and TS 2, the mean fiber lengths and the amount of talcs and glass fibers obtained by experiment were used in the numerical simulation.
3. Theoretical background 3.1 Fiber length distribution (FLD) For fiber reinforced polymer (FRP) composites, the length of fibers can vary due to shear stresses that cause the breakage of the fibers during extrusion and injection molding processes. The thermomechanical properties of FRP composites are affected by the FLDs that can be described with a probability density function (PDF). A cumulative function of the fibers is obtained by integrating the PDF with the fiber lengths ranging from to , which is expressed as below.
= = 1
(1)
where, is the fiber length probability density function. The FLD is well described with a two-parameter statistical function, namely the Weibull distribution function that is described as below.
= exp− > 0 & , > 0
(2)
Here, a is the scale parameter and b is the shape parameter. It is important to consider the FLDs to predict thermomechanical properties of the composites such as stiffness, strength, toughness, fatigue resistance, and thermal expansion coefficient. These thermomechanical properties can vary due to the existence of inclusions since the inclusions induce a stressstrain perturbation in the composites [23, 24]. Once the PDFs are known, the mean fiber length can easily be obtained by
%
$ = = & Γ1⁄ + 1
(3)
where Γ* is the gamma function. By knowing the mean fiber length, scale and shape parameters, the ultimate tensile strength of unidirectional fiber reinforced composites with different FLDs can be estimated.
3.2 Mechanical strength of composites When inclusions such as talcs and glass fibers are introduced into a polymer matrix, average strain near the inclusions is not the same with that of the pure matrix [23, 24]. In our composite system, the amount of strain perturbation induced by talcs is first considered to create an effective matrix (Fig. 1a and 1b). The rule of mixture provides a theoretical upper- and lower-bound on material properties such as the elastic modulus, ultimate tensile strength, thermal conductivity, and electrical conductivity. We use the general rule of $--
mixture of +, = ./ +/, + . +, to create the effective matrix composed of a polymer matrix and talcs. Here, ./ and . are the volume fractions of talcs and matrix, and +/, and +, are the ultimate tensile strengths of talcs and matrix, respectively. The ultimate tensile strength of composites for unidirecionally aligned fibers, +0, , can be estimated by the summation of the fiber length contribution on the composite strength. 2
$--
+0, = ∑2 . + + . +, - -,
(4)
$--
where, .- and . are the volume fractions of fibers and matrix, and +-, and +, are the ultimate strengths of fiber and effective matrix, respectively. The ultimate tensile strength of composites can be replaced with an integral form by combining as below.
$--
$--
+0, = .- ⁄$ +-, + . +, = χ.- +-, + . +,
(5)
Here, χ is a fiber efficiency factor that determines the ultimate tensile strength of composites. For unidirectional discontinuous composites, χ < 1 and determined by the critical fiber length 0 which is given by 0 = 5- +0, /7 , where 5- and 7 are the fiber radius and the interfacial shear stress between matrix and fiber. When the fiber length is uniform, the fiber efficiency factor χ = /20 for < 0 and χ = 1 − 0 /2 for ≥ 0 . However, this condition is not true in real cases since the fibers are broken during the processing. Therefore, it is necessary to consider the fiber length distributions in the composites to predict precise thermomechanical properties. In our case, the fiber length is not uniform and the fibers are distributed in the matrix with talcs. Therefore, the interfacial shear stress between the fibers and the effective matrix will increase with respect to the applied tensile stress. When tensile force is applied to the composite, the fibers act as bridges across the crack plane. When the fiber length is not uniform, χ is modified as below [25].
χ = = :; ⁄20 $ < + ⁄$ :1 − 0 /2<
=
(6)
Here, χ can be obtained if , , 0 and are obtained. These parameters are obtained from experiment. Overall, the composites consist of the effective matrix and the
anisotropic glass fibers with fiber length distributions (Fig. 1c). The ultimate tensile strength of composites is calculated by combining Eq. 5 and Eq. 6.
4. Results and discussion 4.1 Quantification of fiber length distribution Reinforcing fillers are commonly used to improve the mechanical properties of polymer composites. It is well known that glass fibers and carbon fibers can enhance the mechanical strength as much as ten times to fifty times. Different aspect ratios of the inclusions in the polymer matrix affect the concentrated force and shear resistance between the matrix and inclusions. Therefore, it is crucial to examine the effect of FLDs on mechanical properties [16, 26-28]. In this study, glass fibers and talcs are included in TS 1 and TS 2 samples. TS 1 and TS 2 are incinerated under air condition to examine the amount of the inclusions in the multiphase polymer composites. The weight fraction of the inclusion is defined as >? − > − > @ ⁄>? × 100, where >? , >, and > @ are the weight of original sample, the weight of crucible and original sample, and the weight of crucible and residue after incinerating the sample. The total weight fractions of the inclusions in TS 1 and TS 2 were measured to be 29.06 wt% and 37.93 wt% which correspond to 17 vol% and 25 vol%, respectively (Fig. 2). It was also verified by using an inductively coupled plasma (ICP) mass spectrometer that each TS 1 and TS 2 contained almost the same amounts of glass fibers and talcs in each sample (Supplementary Information Fig. 1). Therefore, the total amount of glass fibers in TS 1 and TS 2 composite is 8.5 vol% and 12.5 vol%, respectively.
Since the amount of inclusions embedded in TS 1 and TS 2 is different, their thermomechanical and rheological properties will become different, and the flowability of the composites will also change. It is clear to identify by SEM that TS 1 and TS 2 have glass fibers and talcs, and the glass fibers possess broad length distributions (Fig. 2). It is shown that TS 2 has more amount of glass fibers and talcs in the matrix than in TS 1. However, it is not yet clear to evaluate the FLDs in the matrix. To overcome this issue, the FLDs in the composites were observed by using an X-ray tomographic method. Thin tensile specimens (10 mm in width × 1 mm in height) were produced to generate unidirectional fiber alignments along the flow direction (Fig. 3a). A small piece (10 mm in width × 10 mm in depth × 1 mm in height) was cut at the center of the tensile specimen where unidirectional fiber alignments were produced and a crack takes place. Images of each plane were firstly obtained, and enhanced by controlling the brightness and contrast, transformed into binary images by a thresholding method. The images were stacked along z-axis to reconstruct and analyze the fiber alignment (Fig. 3b and 3c). It was confirmed from the 3D volumetric reconstruction that most of the glass fibers were aligned along the flow direction. Also, the overall length and density of glass fibers in TS 1 seem to be longer and less than in TS 2. Since the FLDs can influence the thermomechanical and rheological properties of products, the quantification of the FLDs should be carried out to understand the relationship between the FLDs and the flowability of molten polymer composites. From the micro-CT images, we experimentally obtained the FLDs (vertical bars in Fig. 3d). It is obvious from the measurement of the probability density functions that the FLDs in TS 1 varies from 10 to 1200 µm while the FLDs in TS 2 ranges from 10 to 500 µm. The
two-parameter Weibull distribution function (Eq. 2) was used to estimate the PDFs of TS 1 and TS 2 composites. The PDFs are useful to evaluate the thermomechanical and local anisotropy of the composites which result in enhanced stiffness, strength, toughness, fatigue resistance, and low thermal expansion coefficients. The experimental results of FLDs are well fitted to Eq. 2, and the relevant parameters are obtained (solid lines in Fig. 3d). FLDs in TS 1 are more broadly distributed than in TS 2, which can support that TS 1 has better mechanical properties. The broad FLDs in TS 1 can also explain big differences in thermal expansion coefficients along the parallel and vertical directions than those of TS 1, which will be explained in section 3.2.
3.2. The effect of inclusions on thermomechanical anisotropy It has been reported that there is an interrelation between the elastic modulus and thermal expansion coefficient of solid materials [29]. The thermomechanical anisotropy of solid materials is of great interest to the engineering field since dimensional stability is important to produce precise engineering components under varying load and temperature. Specially, transversely isotropic glass fibers can generate the anisotropic thermomechanical properties of polymer composites, which requires the characterization of FLDs to understand the role of the inclusions in the composites. Once FLDs are obtained quantitatively by an X-ray tomography, the effective elastic moduli and ultimate tensile strengths of polymer composites can qualitatively be predicted by using statistical FLD functions such as the Weibull distribution, Log-normal, or
Generalized Extreme Value (GEV) functions [16]. We previously reported that FLDs and distribution skewness in polymer composites have significant impacts on the effective elastic moduli of the composites. When glass fibers are included into a polymer matrix, average strains around the fibers are not equal to those of the matrix. Fibers act as bridges transferring interfacial shear stresses between fibers and matrix, which can also be expressed in a similar fashion with the elastic modulus. Therefore, the FLDs of the composites can be a crucial parameter determining their stiffness and ultimate tensile strength. The fiber efficiency factor χ in Eq. 6 was calculated with the FLDs of TS 1 and TS 2 composites experimentally obtained (Fig. 4a). It is confirmed that the value of χ for TS 2 decreases faster than that of TS 1 because the FLDs of TS 2 is more largely skewed (meaning, left-shifted). When the skewness is small, inclusions act as an efficient reinforcement [16]. It is expected that the large skewness of the FLDs for TS 2 may cause low mechanical properties of the composite. In addition, the fibers longer than the critical fiber length 0 have larger contribution to the composite strength than those of short fibers, which means the ultimate tensile strengths of FRP composites decreases with increasing 0 . This is because 0 is inversely proportional to the interfacial adhesion strength [25, 30]. The value of χ rapidly increases with increasing the mean fiber length $ and approaches gradually a plateau level at large mean fiber length (an inset in Fig. 4b). From the χ result, it is anticipated that the ultimate tensile strength of FRP composites would increase significantly until $ reaches 0.2 mm. As expected, the ultimate tensile strength of FRP composites rapidly increases with increasing $ when $ is small, then the increase shows a plateau level around $ = 1 mm (Fig. 4b). In our experiment,
the mean fiber lengths of TS 1 and TS 2 are calculated to be 0.082 mm and 0.05 mm, respectively. From the theory, the tensile strengths of the composites for $ = 0.082 mm and 0.05 mm correspond to +0, = 111 MPa and 98 MPa (see SI Table 2). The experimental results show that the ultimate tensile strengths of TS 1 and TS 2 are around 110 ± 5 MPa and 95 ± 6 MPa, the results of which are in good agreement with the theoretical prediction. One of the possible reasons for higher composite strength for TS 1 than TS 2 is that the overall fiber length in TS 1 are longer than TS 2, promoting good interfacial shear strength 7 between the matrix and fibers, which results in higher ultimate tensile strength of TS 1 than TS 2. It was also reported that the effect of molten polymer flow direction on fatigue behavior for talc-filled composite where the fatigue strength was higher in the longitudinal direction as compared to the transverse to the molten polymer flow direction [31]. The effect was much less as compared to what has been observed for fiber reinforced composites. This behavior can be explained by the concept of a stress transfer length over which the strain in the fiber builds up. Provided that the composite remains fully elastic and there is no interfacial sliding between the fillers and the matrix, the composites with high aspect ratio of the fibers exhibit long stress transfer lengths, providing an efficient reinforcing effect. One of the key factors determining dimensional stability and deflection of polymer composite products is the coefficient of thermal expansion (CTE) [32-34]. Especially, the ratio of anisotropic CTE values strongly influences the warpage and deflection of injection molded polymer composites. A small piece (10 mm in width × 3 mm in depth × 1 mm in height) was cut at the center of the tensile specimen where unidirectional fiber alignments
were produced to measure the CTEs along parallel and vertical directions (An inset in Fig. 5). In our experimental results, there are three unique features to highlight for the CTEs of TS 1 and TS 2 (Fig. 5). First, the CTEs of TS 1 measured in both parallel and vertical directions show higher values than those of TS 2. It is because the total amount of inclusions suspended in TS 2 is higher than TS 1, resulting in the decrease of CTEs upon the temperature change. Second, it is also worthy to note that the CTEs in parallel directions for both TS 1 and TS 2 are much smaller than those in vertical directions. Most of the glass fibers are aligned along the parallel direction to the flow in the composites during the injection molding process while producing the tensile specimens, which hinders the expansion of the composites along the parallel direction. Furthermore, the molecular orientation of LCP itself is also aligned along the parallel direction, which enhances the anisotropy of the CTEs in the composites [34]. Talcs are structurally isotropic reinforcements which do not affect the anisotropy of CTEs of the composites. Third, the difference of the CTEs between parallel and vertical directions for TS 1 is larger than that of TS 2, the result of which can be interpreted from the FLD results. TS 2 shows shorter fiber lengths (meaning, left-shifted FLD distribution) in comparison with TS 1, which induces a small local anisotropy of TS 2 than TS 1 resulting in small increase of the CTEs of the composites.
3.3. The effect of inclusions on glass transition temperature
Since LCPs are highly molecular oriented polymers, they possess unique features such as high mechanical strength at high temperature, extreme chemical resistance, flame retardance, and good flowability. Typically, LCPs show a small glass transition temperature (FG ) than many other polymers due to their high crystallinity, and therefore, the mechanical properties do not significantly change upon the temperature variation. When the inclusions are embedded into the polymer matrix, however, FG changes due to the perturbation of heat capacity caused by the inclusions. FG of pure LCP, TS 1, and TS 2 were examined to characterize the thermodynamic effect of glass fibers on the composites. The samples were first heated up and cooled down as a first cycle to eliminate any thermal history caused during a sample fabrication process. Thereafter, it heated up again to measure the glass transition temperature. It was shown that the pure LCP, TS 1, and TS 2 showed their onsets of FG at 252.97, 246.77, and 240.55 ℃, respectively (Fig 6a – 6c). FG decreases as increasing the amount of inclusions in the LCP matrix. The decrease in the glass transition temperature with high loading of the fillers may indicate the poor interfacial adhesion between the fillers and the matrix. A main reason for the alternation of the glass transition temperature is the changes in the conditions of deformations of the polymer between fillers and the restriction in the molecular mobility due to absorption interaction in polymer surface layers onto filler [35-36]. The formation of an interphase affects the physiochemical properties of the composites. It was also reported that the filler content and the filler size do not significantly affect the glass transition temperature [37]. The existence of reduced FG can lead to poor long term performance of the polymer composites such as lower fracture toughness, durability, and local stress state of the composites [38], which means that TS 1
and TS 2 may have worse long term fracture toughness than the pure LCP matrix even though the tensile strength and elastic moduli are higher than the pure LCP matrix. These results are associated with the fact that the pure LCP matrix already possesses a good toughness while the inclusion reinforced TS 1 and TS 2 composites did not improve the toughness of the composites rather than enhancing the elastic moduli and ultimate tensile strengths only. This behavior is often observed in FRP composites where the polymer matrix has a good fracture toughness so that there is no improvement on the fracture toughness comparing to the pure polymer matrix [38].
3.4. The effect of inclusions on flowability An injection molding process of molten polymer composites is modelled by the finite element method (FEM). The governing equations of the process are the conservations of mass, momentum, and energy, which are described as below. MN M/
+ O∇ ∙ RS = 0
MTS
O M/ = −∇U + ∇ ∙ 7 + OVS MY
M[
OWX M/ = ZF M/ + \]^ ; + ∇ ∙ _S
(7)
(8)
(9)
where O is the density, RS is the velocity vector, P is the pressure, 7 is the viscous stress tensor, VS is the body force vector, WX is the specific heat at constant pressure, Z is the coefficient of thermal expansion, \ is the viscosity, ]^ is the shear rate, and _S is the heat flux.
The molten polymer is considered as a non-Newtonian viscous fluid which can be represented by the Cross-WLF model as below. \=
`a da e^ %i bc ∗ h f
(10)
where \, \? , ]^ , 7 ∗ , and n represent the melt viscosity, the zero shear viscosity, the shear rate, the critical stress level at the transition to shear thinning, and the power law index in high shear rate regime. Flowability is especially an important issue for a micro-injection molding process of small components such as electronic components, connectors, antennas wherein molten polymers pass through extremely narrow channel pitches. The flowability of molten polymers strongly depends on the composition of the polymer composites since the inclusions in the matrix affect their rheological properties and solidification process. We prepared a narrow spiral-shaped mold with the rectangular cross-section of 650 µm in width and 1500 µm in height to measure the flowability of TS 1 and TS 2 composites (Fig. 7a). A flow length is defined as the distance inside the spiral mold through which molten polymers flow until they solidify. It is shown that TS 1 flows farther than TS 2 in the mold until the flow front is solidified (An inset of Fig. 7b). The reinforcing fillers inside the matrix affect the rheological properties of the molten polymers. There are three main parameters that determine the solidification process of molten polymers: thermal conductivity, specific heat, and viscosity of composites. The thermal conductivity and the specific heat of TS 1 and TS 2 are similar so that the viscosity of composites primarily
affects the flowability of the molten composites inside a mold. Processing conditions (e.g., mold temperature, melt temperature, filling and packing pressures) for an injection molding of TS 1 and TS 2 set to be the same to compare only the viscosity effect on the flowability. The viscosity parameters for fitting to the Cross-WLF viscosity model are listed in SI Table 3. It is confirmed that the flowability of TS 1 is better than TS 2 since the viscosity of TS 1 lower than that of TS 2 at low shear rate range under the same temperature (Fig. 7b). When the viscosity of the material is low at certain temperature, the molten polymers can easily be filled into the mold. TS 1 composite with the smaller amount of glass fibers than TS 2 showed a lower viscosity, promoting better flowability (Fig. 7c – 7f). There is a cross-over point at shear rate 4000 s-1, which is thought to occur because the molten composite with relatively short fiber lengths in TS 2 possesses a low friction than TS 1 when the shear rate exceeds a critical point even though the fiber concentration is higher than TS 1. In our experiment, the maximum shear rate occurs in the mold is around 2500 s-1 so that the flowability of TS 1 is still better than TS 2. Also the length of glass fibers does not affect the flowability significantly since the dimensions of the spiral mold are much longer than the fiber lengths. The effect of FLDs will become more critical for a micro-injection molding process where the dimensions of the mold are small and shear rates are extremely high. Overall, this work will help understand the effects of FLDs on thermomechanical anisotropy and rheological properties of polymer composites that are ubiquitous in a variety of industrial applications, and give good insights to improve the processability of polymer
composites during various molten polymer processing such as injection molding, compression molding, resin transfer molding, infusion, and extrusion techniques.
4. Conclusion We investigated the microstructural anisotropy of glass fiber and talc reinforced multiphase polymer composites. The inclusions in the polymer matrix affect the anisotropic thermomechanical properties and rheological behaviors of the composites. The microstructure was analyzed by an X-ray microtomography to investigate the fiber length distributions. The Weibull statistical function was employed to characterize the fiber length distributions. The fiber efficiency factor was calculated by using the statistical function and was used to model the ultimate tensile strength of the composites. It was confirmed that the ultimate tensile strength of the composites increases when the fiber efficiency factor increases due to the long fiber lengths. The theoretical prediction was in good agreement with the experimental result. The thermomechanical anisotropy was evaluated by using linear thermal expansion coefficients. The structural hindrance due to the fibers reduced the thermal expansion along the fiber alignment direction, resulting in thermomechanical anisotropy of the composites. The glass transition temperature was found to decrease with increasing the amount of inclusions into the polymer matrix. The rheological properties of the molten polymer composites were confirmed to be a primary factor in determining the flowability of the composites. This work will help understand the effects of FLDs on thermomechanical anisotropy and flowability, which gives good insights to improve the processability of inclusion reinforced polymer composites.
Acknowledgement This work was supported by Project of convergence/integrated technology development funded by Korea Small and Medium Business Administration in 2015. It was partially supported by Basic Research Program through the National Research Foundation of Korea (NRF)
funded
by
the
Ministry
of
Education,
Science
and
Technology
(2015R1A6A3A03020612 and 2013R1A1A2059827). Also, this work was supported by the Commercializations Promotion Agency for R&D Outcomes (COMPA) funded by the Ministry of Science, ICT and Future Panning (MISP). It was supported by the Industrial Strategic Technology Development Program funded by the Ministry of Trade, Industry and Energy (MI, Korea) [10052641].
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Fig. 1. Schematic illustration of multiphase hybrid composite with talcs and glass fibers. (a) Talcs with polymer matrix, (b) an effective matrix composed of talcs and matrix by the rule of mixture, and (c) a hybrid composite with glass fibers aligned along the tensile direction in the effective matrix. Glass fibers have length distributions and bridge between a crack upon an applied force.
Fig. 2. The characterization of inclusion compositions in (a) TS 1 and (b) TS 2 before and after incineration at 600 ℃ for 24 hours, and SEM images after incineration.
Fig. 3. (a) Tensile specimen of LCP composites (X-ray tomography images are obtained from the red rectangular section sized by10 mm in width × 10 mm in depth × 1 mm in height), (b) and (c) 2D tomographic raw images are image-processed, and then reconstructed to 3D structures to observe the fiber alignments and length distributions. (d) Fiber length distributions of TS 1 and TS 2, and their Weibull function curve fittings. A scale bar is 0.1 mm.
Fig. 4. (a) Effect of critical fiber length on fiber efficiency factor for unidirectional composites of TS 1 and TS 2. (b) Effect of mean fiber length on the ultimate tensile strength of composites of TS 1 and TS 2. An inset graph shows a fiber efficiency factor with
respect
to
the
mean
fiber
length.
Fig. 5. The coefficients of thermal expansion of TS 1 and TS 2 along the parallel and vertical directions with respect to fiber alignment direction. The heating rate is 5 ℃/min.
(Continued.)
Fig. 6. DSC traces of (a) pure LCP, (b) TS 1, and (c) TS 2 during first and second heating stages with the heating rate of 10 ℃/min.
Fig. 7. (a) Flowability test in a spiral-shaped mold by using an injection molding. (b) Viscosities of TS 1 and TS 2 at 350 ℃ used in this study. An inset graph shows the flow length of TS 1 and TS 2 through the spiral-shaped mold. (c), (d) Experimental and numerical results of the flow length of TS 1. (e), (f) Experimental and numerical results of the flow length of TS 2.